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Optimization method for the inverse problem of reconstructing the source term in a parabolic equation. (English) Zbl 1183.65118
The authors consider an inverse problem of reconstructing in the parabolic heat equation a heat source term which depends on the spatial variable using a final temperature measurement. The authors use an optimal control framework to discuss this problem. The existence and a necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer for the cost functional are proved. The Landweber iteration algorithm is applied to the inverse problem and some numerical results are also presented.

65M32Inverse problems (IVP of PDE, numerical methods)
35R30Inverse problems for PDE
49J20Optimal control problems with PDE (existence)
35Q05Euler-Poisson-Darboux equation and generalizations
80A23Inverse problems (thermodynamics)
65M12Stability and convergence of numerical methods (IVP of PDE)
Full Text: DOI
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